Design of Slabs-on-GradeDesign of Slabs-on-Grade

CE A433 – RC DesignCE A433 – RC Design

T. Bart Quimby, P.E., Ph.D.T. Bart Quimby, P.E., Ph.D.

Spring 2007Spring 2007

IntroductionIntroduction

Slabs on grade are PAVEMENTS not Slabs on grade are PAVEMENTS not generally structural elementsgenerally structural elements Pavements pass loads through Pavements pass loads through

compression to the supporting soilcompression to the supporting soil As long as the soils deformations are low, As long as the soils deformations are low,

there is negligible bending in the slabthere is negligible bending in the slab Slabs on grade are deemed to be Slabs on grade are deemed to be

successful if there is little or no successful if there is little or no crackingcracking

PavementPavement

Apply load to top of slab

Since the slab is stiffer than the soil the load is distributed over a

larger area of soil

A thicker slab is stiffer and distributes the load over a

larger area of soil

Types of CracksTypes of Cracks

StructuralStructural Structural cracks are the result of Structural cracks are the result of

subgrade settlement and/or stiffness subgrade settlement and/or stiffness discontinuitydiscontinuity

Often occur when a floor is over loadedOften occur when a floor is over loaded ShrinkageShrinkage

Shrinkage cracks occur soon after a floor Shrinkage cracks occur soon after a floor slab DRIES and will not increase in length, slab DRIES and will not increase in length, width or number after the drying process width or number after the drying process is completed.is completed.

Causes of Structural Causes of Structural CrackingCracking

Virtually all structural cracks are the result Virtually all structural cracks are the result of subgrade failureof subgrade failure

The failure may result from one or more of The failure may result from one or more of the following conditionsthe following conditions The subgrade is improperly designed or The subgrade is improperly designed or

preparedprepared The slab thickness is too thin for applied loads The slab thickness is too thin for applied loads

and the stiffness of the subgradeand the stiffness of the subgrade The concrete does not have sufficient strengthThe concrete does not have sufficient strength

It is necessary to determine the stiffness It is necessary to determine the stiffness of the subgrade and the magnitude of the of the subgrade and the magnitude of the expected loads so that the proper slab expected loads so that the proper slab thickness can be determinedthickness can be determined

Structural CracksStructural Cracks

Cracks form when the Moment exceeds the Cracking Moment

Thickness Design of Slabs on Thickness Design of Slabs on GradeGrade

Slabs on grade are, to a limited extent, Slabs on grade are, to a limited extent, beams on elastic foundations. The beams on elastic foundations. The softer the supporting soil and/or the softer the supporting soil and/or the larger the load, the stronger and stiffer larger the load, the stronger and stiffer the slab must be to spread the load the slab must be to spread the load over more of the supporting soilover more of the supporting soil Slab Slab stiffnessstiffness is a function of slab is a function of slab

thicknessthickness Slab Slab cracking strengthcracking strength is a function of is a function of

concrete strengthconcrete strength and and slab thicknessslab thickness

Thickness Design Thickness Design ProceduresProcedures

Portland Portland Cement Cement AssociationAssociation

Wire Wire Reinforcing Reinforcing InstituteInstitute

Corp. of Corp. of EngineersEngineers

PCI MethodPCI Method

A series of charts for various loading A series of charts for various loading conditions (wheels, racks, posts, etc)conditions (wheels, racks, posts, etc)

Example of slab thickness Example of slab thickness determination for a wheeled vehicle:determination for a wheeled vehicle: Data for lift truckData for lift truck

Axle load = 25 kAxle load = 25 k Wheel spacing = 37 inWheel spacing = 37 in Number of wheels = 2Number of wheels = 2 Tire inflation pressure = 110 psiTire inflation pressure = 110 psi

PCI Example ContinuedPCI Example Continued

Contact area = wheel load/inflation Contact area = wheel load/inflation pressure pressure Contact area = (25,000 lb / 2 wheels) / Contact area = (25,000 lb / 2 wheels) /

110 psi = 114 in110 psi = 114 in22

Subgrade and Concrete DataSubgrade and Concrete Data Subgrade Modulus, k = 100 pciSubgrade Modulus, k = 100 pci Concrete 28-day strength, f’Concrete 28-day strength, f’cc = 7,000 psi = 7,000 psi

Concrete flexural strength, MR ~ 7.5sqrt(f’Concrete flexural strength, MR ~ 7.5sqrt(f’cc) ) ~ 640 psi~ 640 psi

PCI Example ContinuedPCI Example Continued

Use a factor of safety of 2.0Use a factor of safety of 2.0 Choice depends of number of stress Choice depends of number of stress

repetitions permittedrepetitions permitted Concrete working stress = MR/FSConcrete working stress = MR/FS

WS = MR/FS = 640 psi / 2 = 320 psiWS = MR/FS = 640 psi / 2 = 320 psi Slab stress per 1,000 lb of axial loadSlab stress per 1,000 lb of axial load

WS / axle load, kips = 320/25 = 12.8 psi WS / axle load, kips = 320/25 = 12.8 psi per 1,000 lbs.per 1,000 lbs.

PCI Example ContinuedPCI Example Continued

Slab Stress per 1,000 lb of axle load

Effective Contact

Area

Wheel Spacing

Subgrade Modulus

Use 8” Slab

PCI Chart for RacksPCI Chart for Racks

Need to Need to match match criteria for criteria for the chartthe chart

Read the Read the instructions instructions for each for each chart!chart!

Causes of Shrinkage Causes of Shrinkage CrackingCracking

Shrinkage cracking occurs due to the Shrinkage cracking occurs due to the normal volumetric changes normal volumetric changes associated with dryingassociated with drying

Normal concrete can only stretch Normal concrete can only stretch about about 0.0020.002 inches per foot without inches per foot without rupturingrupturing

Normal shrinkage is about Normal shrinkage is about 0.0060.006 ((++25%) inches per foot25%) inches per foot

If the slab is restrained against If the slab is restrained against movement then cracking is inevitablemovement then cracking is inevitable

Minimizing Shrinkage Minimizing Shrinkage CrackingCracking

Shrinkage cracking can be Shrinkage cracking can be minimizedminimized by by Reducing the shrinkage characteristics of Reducing the shrinkage characteristics of

the concrete mixthe concrete mix Reducing restraint on the slabReducing restraint on the slab

Shrinkage cracking can be Shrinkage cracking can be controlledcontrolled by by Encouraging cracks to appear at Encouraging cracks to appear at

predetermined locationspredetermined locations The use of reinforcing steelThe use of reinforcing steel

Reducing Shrinkage Reducing Shrinkage Characteristics of the Concrete Characteristics of the Concrete

MixMix Reduce the volume of water in the mixReduce the volume of water in the mix

The challenge is to limit the amount of The challenge is to limit the amount of water in the mix while maintaining water in the mix while maintaining workability and finishability without workability and finishability without excessive use of water reducersexcessive use of water reducers

Use coarser ground cementUse coarser ground cement Use the largest sized aggregate Use the largest sized aggregate

permitted by designpermitted by design Use shrinkage compensating concreteUse shrinkage compensating concrete

Reducing Shrinkage Reducing Shrinkage Characteristics of the Concrete Characteristics of the Concrete

Mix (Cont.)Mix (Cont.) Use proper curing Use proper curing

techniquestechniques Proper curing keeps Proper curing keeps

water in the concrete water in the concrete until it has achieved until it has achieved sufficient tensile sufficient tensile strength before strength before shrinkage occursshrinkage occurs

Proper curing allows Proper curing allows drying to occur more drying to occur more evenly through the slab evenly through the slab thicknessthickness

CurlingCurling

Differential shrinkage due to drying can result in “curling” of the slab edges, resulting in an induced moment in the slab.

When the moment equals the cracking moment a crack forms, redistributing the stress

Sources of RestraintSources of Restraint

Friction between the slab and the Friction between the slab and the groundground As the slab shrinks, the friction resists As the slab shrinks, the friction resists

the motion, causing tension in the slabthe motion, causing tension in the slab Bearing on other features (walls, Bearing on other features (walls,

foundation, drain pipes, columns, foundation, drain pipes, columns, etc)etc)

Attachment to other featuresAttachment to other features

Friction RestraintFriction Restraint

Axial Stress Diagram

Tensile Capacity

Shrinkage CracksShrinkage Cracks

Axial Stress Diagram

Tensile Capacity

Restraint by Restraint by FeaturesFeatures

Locating “Cracks”Locating “Cracks”

Control and construction joints are Control and construction joints are places of intentional weakness. They places of intentional weakness. They are placed close enough together to are placed close enough together to keep tensile stresses in the slab keep tensile stresses in the slab below the tensile rupture strength of below the tensile rupture strength of the concretethe concrete

Control JointsControl Joints

The purpose of these joints “is to The purpose of these joints “is to predetermine the location of cracks for predetermine the location of cracks for esthetic and performance purposes.” esthetic and performance purposes.” ACI ACI 302.1R, pg 6302.1R, pg 6

““Unless the design provides for the Unless the design provides for the specific supplemental reinforcing across specific supplemental reinforcing across the joint, the resulting induced crack may the joint, the resulting induced crack may offer no structural advantage over a offer no structural advantage over a randomly occuring shrinkage crack.” randomly occuring shrinkage crack.” ACI ACI 302.1R, pg 6302.1R, pg 6

Construction JointsConstruction Joints

These joints “are placed in a slab These joints “are placed in a slab where the concreting operations are where the concreting operations are concluded for the day, generally in concluded for the day, generally in conformity with a predetermined joint conformity with a predetermined joint layout. If at any time concreting is layout. If at any time concreting is interrupted long enough for the interrupted long enough for the placed concrete to harden, a placed concrete to harden, a construction joint should be used.” construction joint should be used.” ACI ACI 302.1R pg 6302.1R pg 6

ContrControl ol

Joint Joint DetailDetail

ss

Construction JointsConstruction Joints

Joint SpacingJoint Spacing

Unreinforced SlabsUnreinforced Slabs 2 to 3 ft for each inch of slab thickness. 2 to 3 ft for each inch of slab thickness.

Smaller aggregate size, higher water Smaller aggregate size, higher water contents, and local experience may contents, and local experience may dictate use of closer jointsdictate use of closer joints

Reinforced SlabsReinforced Slabs Use a subgrade drag equation to Use a subgrade drag equation to

compute joint spacing (See ACI 360R 6.3)compute joint spacing (See ACI 360R 6.3)

Drag EquationDrag Equation

Where:Where: L = distance between joints, ftL = distance between joints, ft AAss = Area of steel per foot width of slab, in = Area of steel per foot width of slab, in22/ftw/ftw ffss = Allowable steel stress (20,000 psi or 24,000 = Allowable steel stress (20,000 psi or 24,000

psi)psi) W = Dead weight of slab, psfW = Dead weight of slab, psf = Friction factor (1 to 2.5)= Friction factor (1 to 2.5)

W

fAL

StrengthfAL

WFriction

ss

allowabless

22

Important Concepts for Joint Important Concepts for Joint DetailsDetails

Only reinforcement across the joint is Only reinforcement across the joint is to be used for vertical load transfer to be used for vertical load transfer only. Use plain bars and coat to only. Use plain bars and coat to prevent bond to concreteprevent bond to concrete

Joint should extend at least ¼ slab Joint should extend at least ¼ slab thickness through the slabthickness through the slab

Vertical load transfer across Vertical load transfer across construction joints can be construction joints can be accomplished with plain bars or accomplished with plain bars or properly designed keyed joints.properly designed keyed joints.

No Vertical Load Transfer

Joints have vertical transfer but allow in

plane shrinkage movement

Controlling Shrinkage Cracking Controlling Shrinkage Cracking with Reinforcing Steelwith Reinforcing Steel

““Reinforcement serves to restrain the Reinforcement serves to restrain the shrinkage, effectively subdividing the slab shrinkage, effectively subdividing the slab and hence distributing the crack area more and hence distributing the crack area more evenly. This produces smaller and more evenly. This produces smaller and more numerous cracks than would occur in an numerous cracks than would occur in an unreinforced slab of the same dimensions. unreinforced slab of the same dimensions. The actual crack area remains essentially The actual crack area remains essentially the same.”the same.” Fricks, T.J. “Cracking in Floor Slabs”, reprinted in Fricks, T.J. “Cracking in Floor Slabs”, reprinted in

ACI SCM-25 (92), pg 122.ACI SCM-25 (92), pg 122.

Reinforcing SteelReinforcing Steel

Smaller bar sizes are better choices than Smaller bar sizes are better choices than large diameterslarge diameters

This steel “should be positioned one-fourth This steel “should be positioned one-fourth the slab thickness below the top surface the slab thickness below the top surface up to 2.0 in maximum.” ACI 302.1R, pg 5up to 2.0 in maximum.” ACI 302.1R, pg 5

Minimum cover of the steel is controlled Minimum cover of the steel is controlled by ACI 318 7.7. by ACI 318 7.7. Top cover ¾” inch clear cover for slabs Top cover ¾” inch clear cover for slabs

protected from the weather, 1.1/2” for #5 or protected from the weather, 1.1/2” for #5 or smaller bars and 2” for larger bars exposed to smaller bars and 2” for larger bars exposed to weatherweather

3” clear between bars and the ground.3” clear between bars and the ground.

Is Is ReinforcemeReinforcement Needed?nt Needed?

Concrete Floors on Ground

By Portland Cement Association

Second Edition

Sample Slab Reinforcing Sample Slab Reinforcing CalculationCalculation

Determine the reinforcing steel Determine the reinforcing steel requirement for an outdoor, 5” thick requirement for an outdoor, 5” thick concrete slab with control joints spaced 25 concrete slab with control joints spaced 25 ft apart. The slab is cast on a compacted ft apart. The slab is cast on a compacted gravelly soil surface. Use 40 ksi rebargravelly soil surface. Use 40 ksi rebar

VariablesVariables ffss = 20,000 psi = 20,000 psi = 2.0 (assume that gravel surface has some = 2.0 (assume that gravel surface has some

interlock with the slab)interlock with the slab) L = 25 ftL = 25 ft W = 5” (150 pcf / 12”) = 62.5 psfW = 5” (150 pcf / 12”) = 62.5 psf

Calculation ContinuedCalculation Continued

From drag equation: From drag equation: Req’d AReq’d Ass = 0.0781 in = 0.0781 in22/ftw/ftw

Spacing Calcs:Spacing Calcs: #3 bar: s #3 bar: s << (.11 in (.11 in22/bar)(12”/ft)/(.0781 in/bar)(12”/ft)/(.0781 in22/ft) = /ft) =

16.9 in16.9 in #4 bar: s #4 bar: s << 30.7 in 30.7 in 6x6 W4.0xW4.0 wire mesh gives A6x6 W4.0xW4.0 wire mesh gives Ass = 0.080 in = 0.080 in22/ftw./ftw. ACI 318 7.6 limits spacing to min(3h, 18”)ACI 318 7.6 limits spacing to min(3h, 18”)

Decision: Use #3 bars 15” O.C. each way. Decision: Use #3 bars 15” O.C. each way. Place with a clear cover of 1” below top of Place with a clear cover of 1” below top of slab.slab.